EM-test for homogeneity in a two-sample problem with a mixture structure

ABSTRACT

In many applications such as case-control studies with contaminated controls, or the test of a treatment effect in the presence of nonresponders in biological experiments or clinical trials, a two-sample problem with one of the samples having a mixture structure often arises. Due to the importance and wide applications of scale mixtures and location mixtures, we consider in this paper the case that the component densities differ only in scale parameters and the case that the component densities differ only in location parameters, and further construct an EM-test for the two-sample problem under each case. We show that both the EM-tests possess a chi-squared null limiting distribution. The local power analysis and sample size calculations are also investigated. Finally, the simulation studies and real data analysis demonstrate that the proposed EM-tests have better performance than the existing methods.

KEYWORDS:

• EM-test
• homogeneity test
• limiting distribution
• scale mixtures
• two-sample problem

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Yuejiao Fu http://orcid.org/0000-0001-8606-570X

Additional information

Funding

Dr. Liu's and Professor Pu's research was supported by grants from the National Natural Science Foundation of China (11801359, 11801210, 11701360, 11771145). Professor Fu's research was supported by Discovery Grant from the Natural Sciences and Engineering Research Council of Canada.